The conductor of a cyclic quartic field using Gauss sums |
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Authors: | Blair K Spearman Kenneth S Williams |
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Institution: | (1) Department of Mathematics and Statistics, Okanagan University College, Kelowna, B.C, Canada, V1V 1V7;(2) Department of Mathematics and Statistics, Carleton University, Ottawa, Ontario, Canada, K1S 5B6 |
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Abstract: | Let Q denote the field of rational numbers. Let K be a cyclic quartic extension of Q. It is known that there are unique integers A, B, C, D such that
where A is squarefree and odd, D=B
2+C
2 is squarefree, B
0 , C
0, GCD(A,D)=1. The conductor f(K) of K is f(K) = 2
l
|A|D, where
A simple proof of this formula for f(K) is given, which uses the basic properties of quartic Gauss sums. |
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Keywords: | |
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